National Oceanic and
Atmospheric Administration
United States Department of Commerce


FY 2000

Analytic theory of tsunami wave scattering in the open ocean with application to the North Pacific Ocean

Mofjeld, H.O., V.V. Titov, F.I. González, and J.C. Newman

NOAA Tech. Memo. OAR PMEL-116, NTIS: PB2002-101562, 38 pp (2000)

A theory is developed to better understand the interaction of tsunami waves with small-scale, submarine topography in the open North Pacific Ocean. The tsunamis are assumed to be linear, long gravity waves at single frequencies. The topography is given simple forms from which explicit formulas can be derived for transmitted, reflected, and scattered waves. This topography includes linear features (escarpments and ridges) and circular seamounts. The theory shows that the most important factor determining the intensity of scattering and reflection is the depth of a feature compared with the depth of the surrounding region. A useful measure of this depth effect is the scattering index S = 1 - Tmin, derived from the theory of lineal ridge scattering. Here Tmin = 2/(1 + ), where [square root] H/H. For a regional depth of H = 5500 m, features with depth shallower than H = 1500 m interact significantly with tsunamis and those shallower than 400 m can have a major effect on these waves. The horizontal extent of a feature, compared with the wavelength, and the angle of incidence also affect the amount of scattering and reflection. Based on these criteria, the Emperor Seamount Chain, the Hawaiian Ridges, the Mid-Pacific Mountains, the Aleutian/Komandorskiye and Kuril Island Arcs, and the Shatsky and Hess Rises scatter and reflect transoceanic tsunamis. This interaction also increases the duration of these tsunamis. Simulating these processes with numerical models requires sufficiently accurate topography and high enough spatial resolution.

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